Fig. 4

The distribution of the Χ2 statistic for the association between QTL and eQTL from a permutation test. This example is from the comparison of eQTL from a meta-analysis of all tissues and the multi-trait GWAS. The enriched and impoverished overlapping QTL and eQTL are shown in positive and negative values, respectively. The theoretical thresholds for a Χ2df = 1 test is 3.84 (enrichment) and − 3.84 (impoverishment) for significance level p < 0.05 as are shown by red dotted lines. The empirical thresholds based on the highest and lowest 5% of values in 10,000 permutation tests, are shown with blue dotted lines. Therefore, in the eQTL meta analysis test, the X2 for an enrichment test should be greater than 6.64 for significance level p < 0.05